Let V and W be vector spaces over F field, dimV=n, and dim W=m. What is the dimension of the vector space L(V,W), and what is an optional basis?
Thank you!
Hint : If we fix $\displaystyle B_V$ and $\displaystyle B_W$ basis of $\displaystyle V$ and $\displaystyle W$ respectively, there is a natural isomorphism $\displaystyle \phi:\mathcal{L}(V,W)\to \mathbb{K}^{m \times n}$ given by $\displaystyle \phi (T)=[T]_{B_V}^{B_W}$ .